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On the Novel Ulam–Hyers Stability for a Class of Nonlinear \(\psi \)-Hilfer Fractional Differential Equation with Time-Varying Delays

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Abstract

In this paper, we present some alternative results concerning the uniqueness and Ulam–Hyers stability of solutions for a kind of \(\psi \)-Hilfer fractional differential equations with time-varying delays. Under some updated criteria along with the generalized Gronwall inequality, the new constructive results have been established in the literature. The derived analysis has the ability to generalize and improve some other results from the literature. As an application, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.

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Acknowledgements

The authors thank the referees for the helpful suggestions. This work was supported by the National Natural Science Foundation of China (Grant no. 11471109).

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Authors and Affiliations

  1. Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), Department of Mathematics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Danfeng Luo

  2. Department of Mathematics, University of Malakand, Lower Dir, Khyber Pakhtunkhwa, Pakistan

    Kamal Shah

  3. Department of Mathematics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Zhiguo Luo

Authors
  1. Danfeng Luo
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  2. Kamal Shah
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  3. Zhiguo Luo
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Correspondence to Zhiguo Luo.

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Luo, D., Shah, K. & Luo, Z. On the Novel Ulam–Hyers Stability for a Class of Nonlinear \(\psi \)-Hilfer Fractional Differential Equation with Time-Varying Delays. Mediterr. J. Math. 16, 112 (2019). https://doi.org/10.1007/s00009-019-1387-x

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  • DOI: https://doi.org/10.1007/s00009-019-1387-x

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